Geodesic
$U$-projection for the adjoint representation of the group $\mathrm{GL}(n,K)$
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 10 (2015), pp. 9-23 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the paper we study rings and fields of invariants for the adjoint representation of the group $\mathrm{GL}(n,K)$ over the field of zero characteristic. The aim of this paper is to construct the special linear operator, we call it $U$-projector, that maps any polynomial on the matrix algebra to an $U$-invariant rational function. In this paper we present two different constructions of $U$-projector. Using the $U$-projector we obtain the system of generators of the field of $U$-invariants of the adjoint representation of the group $\mathrm{GL}(n,K)$. We obtain the system of generators of the field of $U$-invariants for the restriction of the adjoint representation to the subgroup of block-diagonal matrices.
Keywords: field of invariants, adjoint representation, unitriangular group, algebra of invariants, representations of groups, locally nilpotent derivation, system of generators.
Mots-clés : solvable group 
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     title = {$U$-projection for the adjoint representation of the group~$\mathrm{GL}(n,K)$},
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K. A. Vyatkina. $U$-projection for the adjoint representation of the group $\mathrm{GL}(n,K)$. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 10 (2015), pp. 9-23. http://geodesic.mathdoc.fr/item/VSGU_2015_10_a0/

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